The tire-to-road interaction is the dominating factor in generating, or changing, the motion of a wheeled vehicle, and the knowledge of variables related to the tire-to-road interaction is essential for many active safety systems in modern vehicles. Parameters related to the road friction are employed in many modern vehicles. For example, anti-lock braking systems (ABS), electronic stability control systems (ECS), and advanced driver-assistance systems (ADAS), all make extensible use of parameters related to the tire-to-road interaction, in order to provide advanced safety mechanisms.
Stiffness of a tire of the vehicle defines the extent to which the tire resists deformation in response to an applied force. A state of the stiffness of the tires is an important factor in understanding the tire-to-road interaction. To that end, the state of stiffness includes at least one parameter defining an interaction of at least one tire of the vehicle with a road on which the vehicle is traveling, but can include multiple parameters. For example, one parameter relating to the forces generated by the tire-to-road contact is the slip. In a longitudinal case, i.e., in the wheel's forward direction, the slip is defined in terms of the difference of the longitudinal velocity and the rotational speed of the wheel normalized by either the rotational speed of the wheel or the longitudinal velocity, whichever one is greater, i.e., whether the wheel is accelerating or braking. In a lateral case, i.e., in the wheel's lateral direction, the slip is defined in terms of a ratio between the wheel's lateral and longitudinal velocity components.
Another important parameter when determining the tire-to-road interaction is the friction coefficient. Knowledge of the friction coefficient can be used as a supervisory component to the driver, but it can also be utilized in, for example, ABS, ESC, and ADAS. Different tires have different characteristics, and precomputing the parameters can be good as a starting point, or as a nominal value. However, since the road conditions, tire pressure, different loading conditions, tire temperature, and wear on the tire, all affect the characteristics of the tire, precomputing the parameters, which determine the state of stiffness, can cause deficient performance of the above-mentioned active safety systems.
Thus, it is desirable to obtain knowledge about the friction and/or other parameters that can help determining the friction while driving. However, the friction is generally difficult to measure or sense directly during driving; hence, it is usually determined by using indirect friction determination methods, in combination with one or more sensors.
Another parameter of the state of the stiffness of the tires is an initial slope of the force-slip curve. The tire stiffness is in general different in the forward and lateral direction, so there are in general two individual force-slip curves per wheel, possibly depending on each other. The tire stiffness can be used directly in vehicle control systems, such as ADAS; can be used as a supervisory component to a driver, e.g., to alert the driver of abrupt changes in the road surface; can be used to classify the road surface on which the car is traveling; and/or it can be used to determine the friction coefficient.
A number of methods aim to estimate the stiffness of the tires using various optimization techniques. For example, the method described in U.S. Pat. No. 8,065,067 uses bins of collected data to approximate a nonlinear function and minimizing error of friction and tire stiffness using nonlinear optimization. However, the nonlinear optimization is known to be prone to lack of convergence or convergence in a local optimum.
Accordingly, there is a need for a system and a method for determining stiffness of tires of vehicle.